# A Logical Framework with Commutative and Non-commutative Subexponentials

@inproceedings{Kanovich2018ALF, title={A Logical Framework with Commutative and Non-commutative Subexponentials}, author={Max I. Kanovich and Stepan L. Kuznetsov and Vivek Nigam and Andre Scedrov}, booktitle={IJCAR}, year={2018} }

Logical frameworks allow the specification of deductive systems using the same logical machinery. Linear logical frameworks have been successfully used for the specification of a number of computational, logics and proof systems. Its success relies on the fact that formulas can be distinguished as linear, which behave intuitively as resources, and unbounded, which behave intuitionistically. Commutative subexponentials enhance the expressiveness of linear logic frameworks by allowing the…

## 12 Citations

Soft Subexponentials and Multiplexing

- Computer ScienceIJCAR
- 2020

This work introduces a non-commutative substructural system with subexponential modalities controlled by a minimalistic set of rules and employs Lambek’s non-emptiness restriction, which is incompatible with the standard (sub)exponential setting.

Reconciling Lambek's restriction, cut-elimination, and substitution in the presence of exponential modalities

- MathematicsJ. Log. Comput.
- 2020

It is shown that for any system equipped with a reasonable exponential modality the following holds: if the system enjoys cut elimination and substitution to the full extent, then the system necessarily violates Lambek's restriction, and two of the three conditions can be implemented.

Logic, Language, and Security: Essays Dedicated to Andre Scedrov on the Occasion of His 65th Birthday

- MathematicsLogic, Language, and Security
- 2020

An upper Π 1 bound is shown for the fragment of infinitary action logic, in which the exponential can be applied only to formulae of implication depth 0 or 1.

Quantale semantics of Lambek calculus with subexponential modalities

- MathematicsArXiv
- 2019

The polymodal version of Lambek calculus with subexponential modalities initially introduced by Kanovich, Kuznetsov, Nigam, and Scedrov and its quantale semantics is considered and a representation theorem for quantales with quantic conuclei is proved.

Undecidability of a Newly Proposed Calculus for CatLog3

- Computer ScienceFG
- 2019

It is proved that the derivability problem for a fragment of this substructural calculus is algorithmically undecidable.

Dynamic Logic. New Trends and Applications: Third International Workshop, DaLí 2020, Prague, Czech Republic, October 9–10, 2020, Revised Selected Papers

- Computer ScienceDaLí
- 2020

This work identifies a graph structure for events based on their relative dependence of occurence and introduces a generic product update based on the concepts of event model and product update.

Bracket Induction for Lambek Calculus with Bracket Modalities

- Computer ScienceFG
- 2018

This paper shows how parsing can be realised which induces the bracketing structure in backward chaining sequent proof search with Lb, the Lambek calculus with bracket modalities Lb.

The Logic of Action Lattices is Undecidable

- Mathematics2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2019

We prove algorithmic undecidability of the (in)equational theory of residuated Kleene lattices (action lattices), thus solving a problem left open by D. Kozen, P. Jipsen, W. Buszkowski.

The Multiplicative-Additive Lambek Calculus with Subexponential and Bracket Modalities

- Computer ScienceJ. Log. Lang. Inf.
- 2021

A proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser shows that categorial grammars based on them can generate arbitrary recursively enumerable languages.

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